Stabilization Of Uncertain Nonlinear Systems Research Articles

Adaptive Event-Triggered Prescribed-Time Stabilization of Uncertain Nonlinear Systems With Asymmetric Time-Varying Output Constraint

Adaptive Event-Triggered Prescribed-Time Stabilization of Uncertain Nonlinear Systems With Asymmetric Time-Varying Output Constraint

Adaptive Prescribed-Time Stabilization of Uncertain Nonlinear Systems With Unknown Control Directions

Adaptive Prescribed-Time Stabilization of Uncertain Nonlinear Systems With Unknown Control Directions

Strong Prescribed-Time Stabilization of Uncertain Nonlinear Systems by Periodic Delayed Feedback

Strong Prescribed-Time Stabilization of Uncertain Nonlinear Systems by Periodic Delayed Feedback

Simultaneous robust model predictive control and state estimation for nonlinear systems with state‐ and input‐dependent uncertainties

AbstractThe convergence and stability of uncertain nonlinear systems is a challenging problem in the nonlinear control area. Besides, in many practical cases, all states are not measurable and are affected by measurement noise. Based on this motivation, the first objective of this paper is to design a novel output feedback robust model predictive control approach for nonlinear systems with state‐ and input‐dependent uncertainties and measurement noise. This approach combines state estimation and robust model predictive control (MPC) into one min–max optimization and by solving the optimization, these two tasks are performed simultaneously. The studied nonlinear system comprises a linear part, a nonlinear part, and a function that denotes the state‐ and input‐dependent uncertainties. Therefore, the other objective is to reduce the computational complexity; thus, the system's nonlinear term and the aforementioned uncertainties are converted into additional disturbances. Subsequently, the optimization problem becomes a quadratic form, which leads to global convergence with the appropriate selection of objective function weights. Besides, this paper explores the convergence of the closed‐loop system states and the sufficient synthesis conditions to guarantee input‐to‐state stability. The implementation on a numerical example and a CSTR process demonstrate the applicability and reliability of the proposed approach.

Robust fuzzy adaptive stabilization for uncertain nonlinear systems with quantized input and output constraints

In this paper, we study the problem of robust fuzzy adaptive output feedback stabilization for a class of nonlinear systems with quantized input and output constraints. The system under consideration has these characteristics: unknown state mismatch uncertainties and unknown disturbances, and unknown measurement noises. By employing the output filtering transformation, the fuzzy logic system (FLS) approximator, the backstepping, and the high gain observer technique, a non-fragile robust fuzzy adaptive observer and a hyperbolic tangent adaptive controller are presented to guarantee that the closed-loop system is ultimately uniformly bounded and the output is constricted in a prescribed performance curve. The effectiveness of the scheme is verified by numerical simulations.

Intermittent control for stabilization of uncertain nonlinear systems via event-triggered mechanism

<p>This paper studies the finite-time stabilization (FTS) and finite-time contraction stabilization (FTCS) of parameter-uncertain systems subjected to impulsive disturbances by using an event-triggered aperiodic intermittent control (EAPIC) method, which combines aperiodic intermittent control with event-triggered control. By employing the Lyapunov method and linear matrix inequality techniques, sufficient conditions for FTS and FTCS are derived. Additionally, within the finite-time control framework, relationships among impulsive disturbance, intermittent control parameters, and event-triggered mechanism (ETM) thresholds are established under EAPIC to ensure FTS and FTCS. The sequence of impulsive moments is determined by a predetermined ETM, and Zeno phenomena are also excluded. Finally, the effectiveness of the EAPIC approach is demonstrated through two numerical examples.</p>

Discontinuous Adaptive Impulsive Control of Uncertain System With Extension in Stochastic Perturbation and Actuator Saturation.

This article investigates the discontinuous adaptive impulsive control of uncertain linear and nonlinear systems with stochastic perturbations and actuator saturation. Existing literature on adaptive impulsive control schemes adopt continuous state information in designing the continuous adaptive law, which loses the advantages of impulsive control completely. In this article, the discontinuous adaptive law is proposed which only requires the state information be transmitted at impulsive instants, therefore, the communication cost could be reduced and the control system is more practical in implementation. Furthermore, a discontinuous adaptive impulsive control law is derived to realize stabilization of uncertain nonlinear systems with stochastic perturbations and actuator saturation, and the robustness of the closed-loop system with the discontinuous adaptive impulsive control scheme is proved to be effective. Finally, two simulation examples for adaptive impulsive control are presented to verify the accuracy of our results.

Output feedback and adaptive output feedback control design for input-affine nonlinear systems based on Riemannian metrics

This paper deals with output feedback and adaptive output feedback control design for input-affine nonlinear systems on the basis of Riemannian metrics. Firstly, an observer for the considered class of nonlinear systems is proposed. Then, it is shown that by combining the introduced observer with state-feedback controllers in a suitable way, output tracking can be achieved. Moreover, the obtained results are extended to be used for adaptive output feedback stabilization of uncertain nonlinear systems. The introduced adaptive controller is more general than the existing adaptive output feedback ones because it does not assume any constraint on the structure of the system and the parametric uncertainty. Simulation results are presented to verify the effectiveness of the proposed control methods.

Robust stabilization of uncertain nonlinear systems with infinite distributed input delays

This paper studies the robust stabilization problem of a class of uncertain Lipschitz nonlinear systems with infinite distributed input delays. A novel robust predictor feedback controller is developed and the controller gain can be obtained via solving a linear matrix inequality. It is shown that the proposed robust predictor feedback controller can globally exponentially stabilize the concerned uncertain nonlinear system with infinite distributed input delays. The key to the proposed approach is the development of several new quadratic Lyapunov functionals. The obtained results are extended to the case of systems with both multiple constant input delays and infinite distributed input delays. It is noted that the obtained results include some existing results on systems with constant input delays or bounded distributed input delays as special cases. Finally, two examples of Chua’s circuit and spacecraft rendezvous system are presented to illustrate the effectiveness of the proposed robust controllers.

Adaptive finite-time stabilization for uncertain nonlinear systems with unknown control coefficients

Finite-time control owns the advantages of precision and rapidness, preferred by many applications with high performance requirements. Its realization calls for subtle treatments, e.g., the Lyapunov method with low-order terms and homogeneity with negative degree. However, the methods available for finite-time control are based on some basic exclusions and essential restrictions to system uncertainties and nonlinearities. This paper addresses for the first time unknown control coefficients without any known bound, and meanwhile extends system nonlinearities, within the framework of continuous adaptive feedback. The success is typically due to several sets of disparate powers in control design and analysis. Specifically, the nonidentical power-type parameters are introduced in high-gain dynamics, instead of an identical one in the literature, to ensure the stabilizing terms have lower powers than the terms containing uncertainties, enabling finite-time convergence. Thus an adaptive finite-time controller is achieved. New integral-type functions are exploited to make up the important Lyapunov function, which are equipped with different powers to make possible the anticipated performance analysis. The effectiveness of the proposed controller is demonstrated by a simulation example.

Finite-time stabilization for uncertain nonlinear systems with impulsive disturbance via aperiodic intermittent control

This paper ensures finite-time stabilization (FTS) and finite-time contractive stabilization (FTCS) for impulsive systems with time-varying parametric uncertainties by investigating the design of an aperiodic intermittent controller, where uncertain impulsive disturbance is generated at the instants caused by the control action to the plant. Based on the Lyapunov methods, several sufficient conditions are proposed to guarantee the FTS and FTCS. In the framework of finite-time, two relationships between impulsive disturbance, aperiodic control periods, and aperiodic control widths are established to guarantee the FTS and FTCS for the system, respectively. Moreover, such two relationships can potentially increase the freedom of the designed control periods and control widths. Finally, two numerical simulations and a practical application are given to show the validity of the aperiodic intermittent controller.

Global stabilization of uncertain nonlinear systems via fractional-order PID

This work presents a method that analyzes the global stabilization of fractional-order uncertain nonlinear feedback systems classes with fractional-order proportional–integral–derivative (PID) controllers. Two theorems are provided to necessary conditions for global convergence to any desired setpoints by designing controllers. The first theorem addresses a class of second-order time-varying systems controlled by fractional-order PID controllers, which extends the main result about PID (Zhao and Guo, 2017) into fractional-order systems via different analysis methods. The second theorem investigates another class of first-order time-invariant systems regulated by fractional-order proportional–integral (PI) controllers. The method is illustrated on two feedback systems with controllers to ensure the global convergence of the feedback system to desired setpoints.

Global Finite-Time Stabilization for Uncertain Systems With Unknown Measurement Sensitivity.

This article focuses on global finite-time output feedback stabilization for uncertain nonlinear systems with unknown measurement sensitivity. The existence of the continuous measurement error resulting from limited accuracy of sensors invalidates the existing design strategies depending on the use of the precise output in the construction of an observer, which highlights the contribution of this article. Essentially, different from related works, we propose a new finite-time convergent observer by avoiding the use of the information on nonlinearities. By combining the homogeneous domination with the addition of a power integrator method, an output feedback controller composed of multiple nested sign functions is successfully developed. Finally, the effectiveness of the presented scheme is exhibited by a numerical example.

Global output-feedback adaptive stabilization for uncertain nonlinear systems with polynomial growth nonlinearities

In this paper, the problem of global adaptive stabilization by smooth output-feedback is investigated for a class of uncertain nonlinear system with unmeasured states dependent growth. The highlight of the paper lies in that the growth rate with output-dependent polynomial growth and the measurement sensitivity are both unknown, or the dimension of the closed-loop system is significantly reduced. To handle these, a distinct observer with two high-gains is introduced and two dynamic high-gains are updated in the new forms. Motivated by the closely related works, we propose a systematic non-identifier based output feedback control scheme by using the idea of universal control and backstepping technique. The designed controller can globally regulate the states of the original system and the observer while maintaining global boundedness of the closed-loop system. A numerical example is given to demonstrate the effectiveness of the proposed method.

Adaptive Stabilization of Uncertain Nonlinear Systems Under Output Constraint

In this article, we extend the adaptive tracking control to more general nonlinear systems with multiple uncertainties, including output constraint, input delay, unknown parameter, and external disturbances for the first time. Without any growth assumptions, the adaptive backstepping technique is combined with the parameter separation technique to solve the parametric nonlinearities while the related results need to apply restrictive assumptions or use an approximation-based scheme to deal with them. To alleviate the serious uncertainties caused by output constraint and input delay, the barrier Lyapunov function (BLF) and the Pade approximation method are employed in a unified framework when the control coefficient is known. Under the case of the unknown control coefficient, the Nussbaum gain technique is further combined to compensate it. Then, under both cases, universal adaptive state-feedback control strategies merged with rigorous stability analysis are proposed, respectively, which guarantees all the signals are uniformly ultimately bounded. In addition, the reference signal tracks the system output into a compact set of the origin and the constraint of output is not violated. Finally, the proposed controllers are applied to an inverted pendulum system, which demonstrates the designed controller is effective.

Robust Exponential Stabilization for a Class of Nonlinear Uncertain Systems with Time-varying Delays

This paper is concerned with the problem of robust exponential stabilization for a class of nonlinear uncertain systems with time-varying delays. By using appropriately chosen Lyapunov-Krasovskii functional, together with the Finsler’s lemma, sufficient conditions for exponential stability of nonlinear uncertain systems with time-varying delays are proposed in terms of linear matrix inequality (LMI). Then, novel sufficient conditions are developed to ensure the nonlinear uncertain system with time-varying delay is robust exponentially stabilizable in terms of linear matrix inequality with state feedback control. Finally, a numerical example is given to illustrate the efficiency of proposed methods.

On the practical output h-stabilization of nonlinear uncertain systems

This paper investigates the problem of output feedback $h$-stabilization of nonlinear uncertain systems. We construct an output feedback controller that guarantees global uniform practical $h$-stability of the closed-loop system. Our original results generalize well-known fundamental results: practical stability, practical asymptotic stability and practical exponential stability for nonlinear time-varying systems. Finally, two numerical examples are presented to demonstrate the validity of the proposed method.

Active disturbance rejection control approach to output-feedback stabilization of nonlinear system with Lévy noises

Abstract In this paper, the active disturbance rejection control (ADRC) approach, an emerging control approach, is applied to output-feedback stabilization for uncertain nonlinear systems disturbed by external stochastic disturbance. Here the disturbance has the form of an uncertain system driven by both Brownian motion and Levy noises. Firstly, for the sake of estimation for all the states and stochastic disturbance, an efficient extended state observer (ESO) is designed. Then an ESO-based output-feedback control approach and the stability in the mean squared sense are finally developed, respectively. A numerical simulation is also presented to demonstrate the effectiveness of our approach.

Robust Impulsive Observer–Based Stabilization for Uncertain Nonlinear Systems With Sampled–Output

In this letter, the design of an impulsive observer–based control, for a class of nonlinear systems with time–varying uncertainties, is proposed based on the LMI framework. The nonlinearities under consideration are assumed to satisfy local Lipschitz conditions. The observer uses sampled measurements of the system output. A time–varying Lyapunov function is used to give sufficient conditions for the existence of the impulsive observer–based control. The observer and controller gain can be obtained through feasible solutions of the LMIs proposed. The scheme presented here demonstrates that mathematically and through simulation, the proposed approach properly estimates and stabilizes all states.

Local stability and stabilization of uncertain nonlinear systems with two additive time-varying delays

This paper investigates the local stability and stabilization problem of nonlinear time-delay systems subject to parameter uncertainties, which are represented by interval type-2(IT2) T-S fuzzy systems with two additive time-varying delays. Because T-S fuzzy models often represent primitive nonlinear systems well only in the region of validity, local stability and stabilization problems are considered. By constructing a novel Lyapunov–Krasovskii functional and using the matrix inequality scaling approach, a new delay-dependent local stability and stabilization criterion is derived in terms of linear matrix inequalities(LMIs). Using Lyapunov level set, the estimation of attraction domain is also developed. Finally, two numerical examples are employed to verify the effectiveness of proposed methods.